Question:

The values of $m,n$ for which the system of equations $x+y+z=4$, $2x+5y+5z=17$, $x+2y+mz=n$ has infinitely many solutions, satisfy the equation:

$m^2+n^2-mn=39$

$m^2+n^2-m-n=46$

$m^2+n^2+m+n=64$

$m^2+n^2+mn=68$

Step-by-Step Solution

Key Concept: $D=0\Rightarrow m=2$. $D_3=0\Rightarrow n=7$. Check which equation is satisfied.

$m=2$, $n=7$. $m^2+n^2-mn=39$.

Correct Answer: 1